* * * Aveyzan's Power With Base 2! * * *
Exists since 28th April. Allowed are positive and negative exponents without any fractional parts.
Possible values: from 2 to 2.
2 ^ 6 ➜ 26

Right-side digit:
?
Base 10 exponent:
10?
Result in mere JavaScript exponentiation operation
?
Result in scientific notation by Aveyzan
?
Result presented by Aveyzan
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Day Update
19th May 2024 Increased right-side limit to 2150000, in case of huge positive exponents page still may be not responding, but please be patient! Only time is required to await the result. Also added buttons, which add or remove specific values to/from the exponent
15th-18th May 2024 Reorganization of results: added right-side digit, established right-side limit to 280004. Solution, which will be used to display big number in whole ensure increased range (possibly up to 2106).
10th-12th May 2024 Attempts to fix negative exponent powers result (lacking fractional zeros), experiments have been finished on 12th May. In the same day provided shortcut with Enter key instead of pressing the button to process. Another change concerned decrementation and incrementation buttons around exponent selected by user, and their shortcuts via left and right arrows
30th April 2024 Fixed positive exponent powers result; huge result may result to false base 10 exponent result anyway and also, it will take longer to load, so be cautious
29th April 2024 Added base 10 exponent result
28th April 2024 Created this page
This page came to force, as factually calculators mainly focus on presenting a huge number in scientific notation. For example: Microsoft Calculator cannot present numbers above 1032 with precision per digit. Aveyzan's in real life scientific calculator from Casio cannot go above 1010 with skipping scientific notation. In case of powers with base 2: Microsoft Calculator uses scientific notation since 2106, and Casio calculator since 234. Not even single JavaScript exponentiation operation can pass above 21024 - 1 and below 2-1074. With minus 1 (Aveyzan mentions 21024) it is a certain number, which ends with digit 5, like every number 22n - 1, where n ≥ 2.

Back on 21st May 2024, Aveyzan figured out the limit concerning scientific notation in Microsoft Calculator using powers of base 2. After some research, this calculator will sign overflow error: in case of positive exponent since 233219 and in case of negative exponent - since 2-33215 (to clarify it more, results out from range 10-10000 - 1010000 throw this error).

This calculator also has its limits. User is required to wait several seconds, if immense positive or negative exponent has been provided. This is why users are discouraged to go for really big numbers, moreover, result and base 10 exponent may be false. Issue with 22040 example has been fixed - correct answer was actually 10614.

Powers with base 2 are called binary numbers. They find many uses around the world, for example - so-called binary system. This is one of variations of number representation, and it is peculiar from these 2 digits: 0 and 1. The digit placed on the right is 20, which is 1. If it has value 0, whole number won't be odd, but even, and vice versa, when it gets value 1.

...00000000 -> 0
...00000001 -> 1

Next zeros mean next powers with base 2 - exponent is being incremented by then. That means second digit from right means 21, third means 22 and so on.

Powers with base 2 are also used when providing limits to specific types, but mainly numbers. For example: in JavaScript, the highest representable number equals 21024 - 1 (1.797693134862... ● 10308), and least is 2-1074 (4.940656458412... ● 10-324). So-called JavaScript maximum safe integer is 9007199254740991 (253 - 1), and minimum is -9007199254740991 (-253 - 1). Meanwhile in PHP it depends on the architecture: in 32-bit systems the int type can store values from -2147483648 (-231) to 2147483647 (231 - 1), meanwhile in 64-bit systems, this type can have values from -9223372036854775808 (-263) to 9223372036854775807 (263 - 1). In Java, the int type has same value range as PHP with system with 32-bit architecture (-231 - 231-1)

Below table for C/C++, with powers with base 2. Main reason why it has been included instead of another examples is that because this language has many various types.
Type Minimum value Maximum value Size in bits
char, char8_t, int8_t, int_fast8_t, int_least8_t -128 (-27) 127 (27 - 1) at least 8
short, char16_t, int16_t, int_fast16_t, int_least16_t -32768 (-215) 32767 (215 - 1) at least 16
int, char32_t, int32_t, int_fast32_t, int_least32_t -2147483648 (-231; excluding Win16: -215) 2147483647 (231 - 1; excluding Win16: 215 - 1) at least 16 (Win16) or 32 (Win32, Linux, Mac OS)
long -2147483648 (-231; excluding Win32: -263) 2147483647 (231 - 1; excluding Win32: 263 - 1) at least 32 (Win32) or 64 (Linux, Mac OS)
long long, int64_t, int_fast64_t, int_least64_t -9223372036854775808 (-263) 9223372036854775807 (263 - 1) at least 64
__int128* -170141183460469231731687303715884105728 (-2127) 170141183460469231731687303715884105727 (2127 - 1) at least 128*
unsigned char, uint8_t, uint_fast8_t, uint_least8_t 0 255 (28 - 1) at least 8
unsigned short, uint16_t, uint_fast16_t, uint_least16_t 0 65535 (216 - 1) at least 16
unsigned int, uint32_t, uint_fast32_t, uint_least32_t 0 4294967295 (232 - 1; excluding Win16: 216 - 1) at least 16 (Win16) or 32 (Win32, Linux, Mac OS)
unsigned long 0 4294967295 (232 - 1; excluding Win32: 264 - 1) at least 32 (Win32) or 64 (Linux, Mac OS)
unsigned long long, uint64_t, uint_fast64_t, uint_least64_t 0 18446744073709551615 (264 - 1) at least 64
__uint128* 0 340282366920938463463374607431768211455 (2128 - 1) at least 128*
bool - - 1
float subnormal: -2149; normal: -2126 2128 (227) at least 32
double subnormal: -21074; normal: -21022 21024 (2210) at least 64
long double 80-bit: subnormal: -216445; normal: -216382
128-bit: subnormal -216494; normal: -216382
 216384 (2214) at least 80 or 128


Warning: Types highlighted by * aren't standard in C++, they are compiler specific, and for programmers it can have different names, respectively: __int128_t and __uint128_t. See more information about fundamental types on here. In values, where question mark is placed, may not be exact and remain questionable. Values for floating-point types (float, double and long double) are approximate.